+2 for Argentina
I found availability MIA-EZE Dec 25/26 on AA metal and EZE-LIM(stopover)-MIA Jan 6/10 on Lan. You will need a ticket for ORD-MIA (miles or $).
This roundtrip is usually 40k BA + 61.50 (taxes) for each pax but you can use 32k BA + 61.50 (taxes) + 104 (cash for miles).
Other option
WAS-LHR
Take a High Speed Train LHR-CDG for $50 each R/T (it takes just 2 hrs 20 mins) and spend few days in Paris
LHR-WAS
You will need a ticket for ORD-WAS (miles or $).
WAS-LHR-WS is 40K AA miles on BA metal + $176(fees)